Chapter 11: Probability Distributions — Online MCQ Test
MATHS · CLASS 12th · Tamil Nadu State Board
Practice Chapter 11: Probability Distributions with a free chapter-wise online MCQ test.
This chapter covers: Focusing on stochastic processes this chapter details discrete and continuous random variables probability mass and density functions. Students evaluate mathematical expectations m....
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Chapter 11: Probability Distributions — Important Questions & Answers
A random variable that can take only a finite or countable number of values is called a ______.
- A. continuous random variable
- B. discrete random variable
- C. mixed random variable
- D. dependent random variable
Answer: B. discrete random variable
A discrete random variable has a countable set of possible values. This is the standard definition used in probability distributions.
A discrete random variable has a countable set of possible values. This is the standard definition used in probability distributions.
For a probability mass function p(x), which condition must always be true?
- A. p(x) can be negative for some values of x
- B. The sum of all p(x) values is 0
- C. The sum of all p(x) values is 1
- D. p(x) must be greater than 1 for all x
Answer: C. The sum of all p(x) values is 1
A probability mass function must satisfy the total probability condition. Hence, the sum of all probabilities is 1.
A probability mass function must satisfy the total probability condition. Hence, the sum of all probabilities is 1.
If a random variable X takes values 0, 1, and 2 with probabilities 0.2, 0.5, and 0.3 respectively, then E(X) is
- A. 0.9
- B. 1.1
- C. 1.3
- D. 1.5
Answer: B. 1.1
E(X) = Σxp(x) = 0×0.2 + 1×0.5 + 2×0.3 = 1.1. This is the weighted average of the values.
E(X) = Σxp(x) = 0×0.2 + 1×0.5 + 2×0.3 = 1.1. This is the weighted average of the values.
A fair coin is tossed 4 times. If X denotes the number of heads, then the distribution of X is
- A. Poisson with λ = 4
- B. Binomial with n = 4 and p = 1/2
- C. Normal with mean 2
- D. Geometric with p = 1/2
Answer: B. Binomial with n = 4 and p = 1/2
The number of heads in a fixed number of independent coin tosses follows a binomial distribution. Here n = 4 and p = 1/2.
The number of heads in a fixed number of independent coin tosses follows a binomial distribution. Here n = 4 and p = 1/2.
A Poisson distribution with parameter λ is used to approximate a binomial distribution when
- A. n is small and p is large
- B. n is large and p is small
- C. n = p
- D. p = 1/2 always
Answer: B. n is large and p is small
The Poisson distribution is a good approximation to the binomial when the number of trials is large and the probability of success is small. In such cases, λ = np.
The Poisson distribution is a good approximation to the binomial when the number of trials is large and the probability of success is small. In such cases, λ = np.